Reading a flash memory by constrained decoding

ABSTRACT

To read memory cells that have been programmed to store an ECC codeword, with each cell storing a respective plurality of bits of the codeword, a respective value of an operational parameter such as a threshold voltage of each cell is measured. Each bit is assigned a respective metric, such as a LLR estimate of the bit, based at least in part on the respective value of the operational parameter of the bit&#39;s cell. The metrics are decoded with reference both to the ECC and to mutual constraints of the metrics within each cell that are independent of the ECC.

This patent application is a continuation-in-part of U.S. patent application Ser. No. 12/407,098 that claims the benefit of U.S. Provisional Patent Application No. 61/074,698 filed Jun. 23, 2008

FIELD AND BACKGROUND OF THE INVENTION

Disclosed herein are methods of reading the cells of a memory and related memory devices, memory controllers and memory systems.

Various physical phenomena occurring in flash memories result in corruption of the stored information. These phenomena include programming noises, read noises, charge leakage over time, wearing of the memory cells due to program and erase cycles etc. In order to allow reliable operation of a flash memory under these conditions, redundant data are stored together with the information, allowing one to correct the errors that corrupted the stored information.

An efficient scheme for inferring the information stored in a flash memory from the read data should provide maximal error correction capability (i.e. allow inferring the stored information under the most severe flash memory noise conditions possible given that a fixed amount of redundant data is used). This allows efficient utilization of the flash memory because a minimal amount of redundancy needs to be used in order to provide reliable storage under given flash memory noise conditions.

Conventionally, the following solutions to this problem have been applied:

1) Tracking Cell Voltage Distributions (CVD)

The statistical distribution of the threshold voltages (or the read voltages) of programmed cells is not fixed for all cells and is not fixed over time. The CVD may change between devices, blocks or pages. The CVD can change as a function of threshold voltages of neighboring cells along the word line (WL) or bit line (BL) due to cross coupling effects or to program disturb (PD) effects. More importantly, the CVD can change over time, due to wearing of the cells by program/erase cycles and due to charge leakage. Knowing the CVD of the cell population to which a read cell belongs is important for several reasons:

-   -   A. The CVD can be used for determining optimal reading         thresholds that should be used when reading the cell, which will         result in a minimal error probability in determining the         programmed cell state.     -   B. The CVD can be used for calibrating Error Correction Code         (ECC) parameters and inputs—computing accurate bit estimations         which are used as an input for a soft ECC decoder requires         knowing the actual CVD model and parameters. Moreover, the CVD         provides an indication of the flash memory noises that affect         the cell and the expected cell error rate (i.e. the probability         that the cell is read at a state different from the state it was         programmed to).         This can be used in order to determine the required decoding         mode, as taught for example in US Patent Application Publication         No. 2007/0124652 and in U.S. patent application Ser. No.         12/124,192, and in order to determine the required reading         resolution (higher reading resolution incurs time and energy         consumption penalties and is not required if low error         probability is expected).

Various conventional schemes for CVD tracking are known. CVD tracking schemes for compensating charge leakage effects due to program/erase wearing and time are described in U.S. patent application Ser. No. 11/941,945. These schemes can be performed in a “blind” manner in which the cells' programmed states are unknown and CVD parameters estimation is done by analyzing the empirical histogram of read voltages of a group of cells (for example the cells of one page). Alternatively, CVD parameter estimation can be performed based on reference cells that are programmed to known states and that are assumed to have the same CVD as the data cells. A disadvantage of the use of reference cells is that it requires allocating specific cells for CVD tracking which cannot be used for storing data. CVD tracking schemes for compensating the electric field effect of neighboring cells are described in U.S. patent application Ser. No. 11/860,553 and in U.S. patent application Ser. No. 12/363,554. In these schemes the parameters of the CVD of a cell are updated according to the read voltages of neighboring cells.

2) Compute Soft Bit Estimations

State of the art ECCs can utilize reliability information on the stored bits in order to improve error correction capability. Such “soft” bit estimations can be computed based on knowing the CVD (i.e. a statistical model for CVD and its parameters). The more accurately the CVD is estimated, the more accurate the soft bit estimations can be. This is why CVD tracking is important. The “soft” information also becomes more accurate when higher resolution reading is used (i.e. when the cell threshold voltage is determined more accurately). Conventional soft bit estimation is described in US Patent Application Publication No. 2007/0086239, in U.S. patent application Ser. No. 11/941,945 and in U.S. patent application Ser. No. 11/860,553.

3) Efficient ECC

Using an efficient ECC that can utilize soft information and that allows correcting maximal number of bit errors with a given ECC redundancy. Examples of conventional ECC use is taught in US 2007/0124652 and in U.S. patent application Ser. No. 12/124,192.

Conventionally, the three mechanisms described above are applied separately, one after another, i.e. first CVD tracking is performed, then a page is read based on the CVD parameters, then soft estimations of the stored bits are computed based on the CVD parameters, and finally ECC decoding is performed on the soft bit estimates.

To summarize, the conventional approach is:

1) CVD tracking computes CVD parameters based only on the read cell voltages.

2) Soft bit estimates for a given cell are computed based only on the read cell voltages and the estimated CVD parameters.

3) Estimates of the stored bits are computed using an ECC decoder which operates only on soft bit estimates.

SUMMARY OF THE INVENTION

The conventional separation between CVD tracking, soft bit estimates computation and ECC decoding results in a suboptimal scheme with degraded error correction capability.

Described herein is a first scheme that performs joint CVD tracking and ECC decoding. One difference between this scheme and the conventional approach is that according to the first scheme described herein the CVD parameters are computed as a function of the read cell voltages under the assumption that the bits stored in the cells belong to valid ECC codewords (relative to the codebook of codewords that is used for encoding the stored data), while conventionally no such assumption is made about the stored bits.

According to some embodiments of the first scheme, an iterative scheme is used such that CVD tracking block and ECC decoding blocks exchange information iteratively. In these embodiments, one feature that differentiates the first scheme from the prior art is the use of feedback from the ECC decoder to the CVD tracking. More specifically, at least for some cells the CVD parameters are computed a second time based on ECC decoder outputs and at least some bit estimates are updated in a second ECC decoding step based on the updated CVD parameters.

Also described herein is a second scheme that performs ECC decoding subject to constraints in addition to the constraint that the output of the decoder must be a valid codeword. Specifically, this scheme imposes constraints associated with which bits are stored in which cells. The two schemes optionally may be combined, to constrain the ECC decoding both by the CVD estimation and by the knowledge of which bits are stored together in commonly shared cells.

One embodiment provided herein is a method of reading a plurality of memory cells that have been programmed to store a codeword of an error correction code, with each cell storing a respective plurality of bits of the codeword, including: (a) measuring a respective value of an operational parameter of each cell; (b) assigning each bit of each cell a respective metric, based at least in part on the respective value of the operational parameter of the each cell; and (c) decoding the metrics with reference both to the error correction code and to mutual constraints of the metrics within each cell that are independent of the error correction code.

Another embodiment provided herein is a memory device including: (a) a plurality of cells for storing a codeword of an error correction code, with each cell storing a respective plurality of bits of the codeword; (b) circuitry for measuring a respective value of an operational parameter of each cell; and (c) a controller operative: (i) to instruct the circuitry to measure the values of the operational parameters, (ii) to assign each bit of each cell a respective metric, based at least in part on the respective value of the operational parameter of the each cell, and (iii) to decode the metrics with reference both to the error correction code and to mutual constraints of the metrics within each cell that are independent of the error correction code.

Another embodiment provided herein is a memory controller, for a memory that includes a plurality of cells for storing a codeword of an error correction code, with each cell storing a respective plurality of bits of the codeword, the memory controller including: (a) a measurement functional block for obtaining, from the memory, for each cell, a measurement of a respective value of an operational parameter of the cell; (b) an assignment functional block for assigning each bit of each cell a respective metric, based at least in part on the respective value of the operational parameter of the each cell; and (c) a decoder for decoding the metrics with reference both to the error correction code and to mutual constraints of the metrics within each cell that are independent of the error correction code.

Another embodiment provided herein is a system for managing a first memory that includes a plurality of cells for storing a codeword of an error correction code, with each cell storing a respective plurality of bits of the codeword, the system including: (a) a second memory for storing program code for: (i) obtaining, from the first memory, for each cell, a measurement of a respective value of an operational parameter of the cell, (ii) assigning each bit of each cell a respective metric, based at least in part on the respective value of the operational parameter of the each cell, and (iii) decoding the metrics with reference both to the error correction code and to mutual constraints of the metrics within each cell that are independent of the error correction code; and (b) a processor for executing the code.

Another embodiment provided herein is a computer-readable storage medium having computer-readable code embodied on the computer-readable storage medium, the computer-readable code for managing a memory that includes a plurality of cells for storing a codeword of an error correction code, with each cell storing a respective plurality of bits of the codeword, the computer-readable code including: (a) program code for obtaining from the memory, for each cell, a measurement of a respective value of an operational parameter of the cell; (b) program code for assigning each bit of each cell a respective metric, based at least in part on the respective value of the operational parameter of the each cell; and (c) program code for decoding the metrics with reference both to the error correction code and to mutual constraints of the metrics within each cell that are independent of the error correction code.

The general method for implementing the second scheme is a method of reading a plurality of memory cells that have been programmed to store a codeword of an error correction code, with each cell storing a respective plurality of bits of the code. A respective value of an operational parameter, such as a threshold voltage, of each cell, is measured. Each bit of each cell is assigned a respective metric such as a soft estimate of the value of the bit. Preferably, the soft estimates are log likelihood ratio estimates. The metrics are decoded with reference both to the error correction code (the result of the decoding should be a valid codeword of the error correction code) and to mutual constraints of the metrics within each cell that are independent of the error correction code, i.e., independent of the requirement that the output of the decoding be a valid codeword of the error correction code.

Preferably, the metrics are assigned in accordance with a cell distribution model of the operational parameter. More preferably, the method also includes updating the cell distribution model in accordance with the decoding. Most preferably, the decoding and the updating are repeated without repeating the measuring of the respective values of the operational parameter.

Preferably, the decoding produces extrinsic estimates of the metrics.

A memory controller for implementing the general method includes three functional blocks. The first functional block is a measurement functional block for obtaining, from the memory, for each cell, a measurement of a respective value of the operational parameter of the cell. The second functional block is an assignment functional block for assigning each bit of each cell a respective metric, based at least in part on the respective value of the operational parameter of the cell. The third functional block is a decoder for decoding the metrics with reference both to the error correction code and to mutual constraints of the metrics within each cell that are independent of the error correction code.

A memory device that corresponds to the general method includes a plurality of cells for storing the codeword, with each cell storing a respective plurality of bits of the codeword. The memory device also includes circuitry for measuring a respective value of the operational parameter of each cell and a controller that implements the general method.

A system, for managing a first memory that includes a plurality of cells, and that corresponds to the general method, includes a second memory and a processor. The second memory is for storing code for implementing the general method. The processor executes the code. A computer readable storage medium that corresponds to the general method has embedded thereon computer code for managing a memory that includes a plurality of cells using the general method.

BRIEF DESCRIPTION OF THE DRAWINGS

Various embodiments are herein described, by way of example only, with reference to the accompanying drawings, wherein:

FIG. 1 is a schematic diagram of iteration between CVD parameter computation and ECC decoding without separate cancellation of cross-coupling;

FIG. 2 is a schematic diagram of iteration between CVD parameter computations and ECC decoding with separate cancellation of cross-coupling;

FIG. 3 is a factor graph that is equivalent to FIG. 1;

FIG. 4 is a high-level schematic block diagram of a flash memory device;

FIGS. 5, 6 and 10 show three embodiments of the controller of FIG. 4;

FIG. 7 is a high-level schematic block diagram of a system for managing a flash memory device;

FIG. 8 shows an exemplary tripartite graph for decoding constrained by knowledge of which bits are stored together in commonly shared cells;

FIG. 9 is a schematic diagram of iteration between a-priori soft bit estimation and ECC decoding.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

The principles and operation of joint CVD estimation and ECC according to the present invention may be better understood with reference to the drawings and the accompanying description.

Let us assume that we are using an error correction code C, such that each set of information bits is mapped into a valid codeword cεC. Furthermore, assume that a set of valid codewords is stored in a set of M cells. This is done by mapping the codewords into a vector s=[s₁ s₂ . . . s_(M)], such that s_(i)εS and S={S₁, S₂, . . . , S_(L)} and L is the number of levels that can be programmed to a flash memory cell (i.e. in a one-bit-per-cell flash memory L=2, in a two-bit-per-cell flash memory L=4, in a four-bit-per-cell flash memory L=16). Then, s_(i) is programmed to the i'th cell. Furthermore, let us denote the read voltages of the set of M cells by the vector v=[v₁ v₂ . . . v_(M)]. Note that because cell reading is quantized in practical flash memory devices, v_(i) can take only a finite set of K values {V₁, V₂ . . . V_(K)}, where K is a function of the reading resolution and higher resolution corresponds to higher K.

We define that a cell's read voltage is v if the actual cell threshold voltage v_(th) satisfies: LTH(v)≦v_(th)≦UTH(v), where LTH and UTH are a functions that match lower and upper reading thresholds for each of the K possible reading voltages {V₁, V₂, . . . V_(K)}. This means that the cell's transistor is open (‘1’) when threshold voltage UTH(v) is loaded on the cell's transistor control gate while the cell's transistor is closed (‘0’) when LTH(v) is loaded on the cell's transistor control gate.

Denote the CVD of a cell as the probability density function ƒ(v) providing the probability of reading the cell at each possible voltage v. Note that the CVD “of a cell” actually is the CVD of a population of cells to which the cell belong. The typical example of such a population is a population of cells whose threshold voltages are disturbed similarly by neighboring cells. Usually, we have a statistical model for the CVD of the cell with parameters θ. For example we can model the CVD of a cell by a Gaussian Mixture Model (GMM), such that the probability of a cell to be programmed to state S_(j) (jε{1, . . . , L}) is λ_(j) and the voltage distribution of the cell given that it was programmed to state s_(i) is normally distributed with expectation μ_(j) and standard deviation σ_(j):

$\begin{matrix} {{{f\left( {v\underset{\_}{\theta}} \right)} = {\sum\limits_{j = 1}^{L}\; {\lambda_{j}{\int_{{LTH}{(v)}}^{{UTH}{(v)}}{\frac{1}{\sqrt{2{\pi\sigma}_{j}^{2}}}^{- \frac{{({v^{\prime} - \mu_{j}})}^{2}}{2\sigma_{j}^{2}}}\ {v^{\prime}}}}}}},{{{where}\mspace{14mu} \underset{\_}{\theta}} = \begin{bmatrix} \lambda_{1} & \ldots & \lambda_{L} & \mu_{1} & \ldots & \mu_{L} & \sigma_{1} & \ldots & \sigma_{L} \end{bmatrix}}} & (1) \end{matrix}$

Preferably, a scrambling mechanism is used in order to randomize the stored bits prior to programming, as described in US Patent Application Publications Nos. 2008/0151618 and 2008/0215798. In that case we can assume that all programmed states are equally probable, i.e. ∀jε{1, . . . L} λ_(j)=1/L and

$\begin{matrix} {{{f\left( {v\underset{\_}{\theta}} \right)} = {\frac{1}{L}{\sum\limits_{j = 1}^{L}\; {\int_{{LTH}{(v)}}^{{UTH}{(v)}}{\frac{1}{\sqrt{2{\pi\sigma}_{j}^{2}}}^{- \frac{{({v^{\prime} - \mu_{j}})}^{2}}{2\sigma_{j}^{2}}}\ {v^{\prime}}}}}}},{{{where}\mspace{14mu} \underset{\_}{\theta}} = \begin{bmatrix} \mu_{1} & \ldots & \mu_{L} & \sigma_{1} & \ldots & \sigma_{L} \end{bmatrix}}} & (2) \end{matrix}$

The CVD parameters θ of the cell can be functions of the charge stored in the neighboring cells, which is manifested in the read voltages of the neighboring cells. So, in general the CVD of the i'th cell, is given by ƒ(v|θ _(i)) where θ _(i) are the CVD parameters of the i'th cell which are a function of the read voltages of the neighboring cells of the i'th cell.

We estimate the CVD parameters θ=[θ ₁ θ ₂ . . . θ _(M)] of each cell from the set of M read cells as a function of the vector of read voltages v=[v₁ v₂ . . . v_(M)] and under the assumption that the underlying bit sequence stored in the M cells is composed of a set of valid codewords (i.e. composed of bit sequences cεC). Based on these CVD parameters we can get optimal estimates for the stored bits through a process of ECC decoding.

Obtaining a closed form expression for the CVD parameters under the assumption that the stored bits belong to valid codewords is usually difficult. An approximate computation can be done instead that uses an iterative method for jointly estimating the CVD parameters and the stored bits.

The idea is to iterate between a block that computes the CVD parameters and a block that performs ECC decoding until convergence to a valid set of codewords is obtained. The incentive for this approach is that CVD parameters estimation is more accurate and less complex if we know the stored bits (or programmed states) and on the other hand ECC decoding of the stored bits is more likely to succeed and more likely to require less operations if accurate CVD parameters are available. By iteratively exchanging information between the CVD parameters estimation block and the ECC decoding block we increase the probability of overall success in recovering the stored bits and we can simplify each of the blocks and shorten the overall convergence time of the scheme to the correct solution.

Referring now to the drawings, FIG. 1 is a schematic diagram of this iteration between CVD parameter computation and ECC decoding.

In FIG. 1 we use the following notation:

1) v=[v₁ v₂ . . . v_(M)] the vector of voltages read from the M cells.

2) {circumflex over (θ)}=[{circumflex over (θ)} ₁ {circumflex over (θ)} ₂ . . . {circumflex over (θ)} _(M)] is the estimate of θ (the CVD parameters of each cell).

3) L _(a)=[L _(a1) L _(a2) . . . L _(aM)] is a vector of a-priori soft estimates of the states s=[s ₁ s ₂ . . . s _(M)] programmed to the M cells. Such soft estimates can be expressed in various ways. One common way is to provide the probabilities for each possible cell state S={S₁, S₂, . . . , S_(L)} given that the cell's read voltage is v, i.e. L _(ai)=[Pr(v_(i)|s_(i)=S₁,{circumflex over (θ)} _(i)) . . . Pr(v_(i)|s_(i)=S_(L),{circumflex over (θ)} _(i))]. Another common way is to use Log-Likelihood Ratio's (LLRs). In this case L _(ai) is given by:

$\begin{matrix} {{\underset{\_}{L}}_{ai} = \left\lbrack {\log \frac{\Pr \left( {{v_{i}s_{i}} = {S_{1,}{\overset{\bigwedge}{\underset{\_}{\theta}}}_{i}}} \right)}{\Pr \left( {v_{i}{s_{i} \neq {S_{1,}{\overset{\bigwedge}{\underset{\_}{\theta}}}_{i}}}} \right)}\mspace{14mu} \ldots \mspace{14mu} \log \frac{\Pr \left( {{v_{i}s_{i}} = {S_{L,}{\overset{\bigwedge}{\underset{\_}{\theta}}}_{i}}} \right)}{\Pr \left( {v_{i}{s_{i} \neq {S_{L,}{\overset{\bigwedge}{\underset{\_}{\theta}}}_{i}}}} \right)}} \right\rbrack^{\prime}} & (3) \end{matrix}$

Without loss of generality we assume in the following that LLR soft estimates are used.

4) L _(d)=[L _(d1) L _(d2) . . . L _(dM)] is a vector of a-posteriori soft estimates (after ECC decoding) of the states s=[s₁ s₂ . . . s_(M)] programmed to the M cells. Assuming LLR soft estimates, L _(di) is given by:

$\begin{matrix} {{\underset{\_}{L}}_{di} = \begin{bmatrix} {\log \frac{\Pr \left( {\underset{\_}{v},{{{\underset{\_}{c} \in C}s_{i}} = {S_{1,}\overset{\bigwedge}{\underset{\_}{\theta}}}}} \right)}{\Pr \left( {\underset{\_}{v},{{\underset{\_}{c} \in C}{s_{i} \neq {S_{1,}\overset{\bigwedge}{\underset{\_}{\theta}}}}}} \right)}\mspace{14mu} \ldots} \\ {\log \frac{\Pr \left( {\underset{\_}{v},{{{\underset{\_}{c} \in C}s_{i}} = {S_{L,}\overset{\bigwedge}{\underset{\_}{\theta}}}}} \right)}{\Pr \left( {\underset{\_}{v},{{\underset{\_}{c} \in C}{s_{i} \neq {S_{L,}\overset{\bigwedge}{\underset{\_}{\theta}}}}}} \right)}} \end{bmatrix}^{\prime}} & \left( {4A} \right) \end{matrix}$

where cεC indicates that the bit sequences stored in the M cells correspond to valid codewords.

5) L _(e)=[L _(e1) L _(e2) . . . L _(eM)] is a vector of extrinsic soft estimates of the states s=[s₁ s₂ . . . s_(M)] programmed to the M cells. An extrinsic estimate of a cell's state is an estimate which is not based on the read cell voltage and its estimated CVD parameters. Assuming LLR soft estimates, L _(ei) is given by:

$\begin{matrix} {{\underset{\_}{L}}_{ei} = \left\lbrack \frac{\log \frac{\Pr \left( {{\underset{\_}{v}}_{\lbrack i\rbrack},{{{\underset{\_}{c} \in C}s_{i}} = {S_{1,}{\overset{\bigwedge}{\underset{\_}{\theta}}}_{\lbrack i\rbrack}}}} \right)}{\Pr \left( {{\underset{\_}{v}}_{\lbrack i\rbrack},{{\underset{\_}{c} \in C}{s_{i} \neq {S_{1,}{\overset{\bigwedge}{\underset{\_}{\theta}}}_{\lbrack i\rbrack}}}}} \right)}\mspace{14mu} \ldots}{\log \frac{\Pr \left( {{\underset{\_}{v}}_{\lbrack i\rbrack},{{{\underset{\_}{c} \in C}s_{i}} = {S_{L,}{\overset{\bigwedge}{\underset{\_}{\theta}}}_{\lbrack i\rbrack}}}} \right)}{\Pr \left( {{\underset{\_}{v}}_{\lbrack i\rbrack},{{\underset{\_}{c} \in C}{s_{i} \neq {S_{L,}{\overset{\bigwedge}{\underset{\_}{\theta}}}_{\lbrack i\rbrack}}}}} \right)}} \right\rbrack^{\prime}} & (5) \end{matrix}$

where v _([i]) is the vector v excluding v_(i) and θ _([i]) is the vector θ excluding θ _(i). Using extrinsic soft estimates in iterative schemes is well known. Using extrinsic soft estimates improves the performance of the scheme by preventing a situation of “self conviction”. In other words, we want to avoid a situation that the CVD parameters estimation block estimates the CVD parameters of the i'th cell θ _(i) based on its own previous estimation.

6) ĉ ₁, ĉ ₂, . . . is the ECC decoder output, where ĉ _(j) the estimate for the j'th codeword stored in the M cells.

The following blocks appear in FIG. 1:

1) CVD Parameters Estimation Block

This block estimates the CVD parameters for each cell based on the read cell voltages and based on estimates of the cells' programmed states. In general, CVD parameters of a cell, given that it was programmed to state s and given that its neighbors read voltages are v _(n), can be computed by examining the statistics of all the cells that were programmed to state s whose neighbors' read voltages are v _(n). In simple cases the cell's neighbors' read voltages do not affect the CVD of the cell—this is usually the case if cross coupling effects between a cell and its neighbors are mitigated by using a multi-step programming plan as taught e.g. in U.S. Pat. No. 6,781,877. In this ease we need to estimate a single set of CVD parameters for all cells. In any case, one can see that computation of the CVD parameters can be simplified if an estimation of the programmed cells' states is available.

According to one exemplary embodiment, hard decisions on the cells' states are used: for the i'th cell we estimate the programmed state ŝ_(i) as the state which is most probable according to L _(ei), i.e.

${\hat{s}}_{i} = {\arg {\max\limits_{s}{{\underset{\_}{L}}_{ei}.}}}$

Based on the programmed state estimates ŝ=[ŝ₁ . . . ŝ_(M)], CVD parameters can be estimated more easily, because we can differentiate between the cell voltage distributions of different states.

Consider as an example the GMM model, described in (2). Let θ _(i)=[μ_(i,1) . . . μ_(i,L) σ_(i,1) . . . σ_(i,L)] denote the unknown CVD parameters of the i'th cell, where μ_(i,j) and σ_(i,j) are the expectation and standard deviation of the voltage distribution of j'th state of the i'th cell, respectively. Furthermore, let v _(n(i)) denote the read voltages of the neighbors of the i'th cell—for example the 3 physically closest neighboring cells which have the strongest cross coupling and/or the strongest program disturb with the i'th cell can be considered. In this case v _(n(i))=[v_(n(i),1) v_(n(i),2) v_(n(i),3)]. Finally, let M(j)={i′|s _(i′)=S_(j)}, ∀jε{1, . . . L} be the set of cells among the M cells for which we estimated the programmed state j and denote by |M(j)| its cardinality

$\begin{matrix} {\left( {{i.e.{\sum\limits_{j = 1}^{L}\; {{M(j)}}}} = M} \right).} & \; \end{matrix}$

Then we can estimate the CVD parameters of the i'th cell, using Linear Minimal Mean Square Error (LMMSE) estimation, as follows:

{circumflex over (μ)}_(i,j)={circumflex over (μ)}_(j) +Ĉ _(j,n) ·Ĉ _(n) ⁻¹·( v _(n(i))−{circumflex over (μ)})

{circumflex over (σ)}_(i,j)={circumflex over (σ)}_(j) −Ĉ _(j,n) ·Ĉ _(n) ⁻¹ ·Ĉ* _(j,n)  (6)

where

$\begin{matrix} {{{\hat{\mu}}_{j} = {\frac{1}{{M(j)}}{\sum\limits_{i^{\prime} \in {M{(j)}}}^{\;}\; v_{i^{\prime}}}}},{\hat{\mu} = {\frac{1}{L}{\sum\limits_{j = 1}^{L}\; {\hat{\mu}}_{j}}}},{{\hat{\sigma}}_{j} = {\frac{1}{{{M(j)}} - 1}{\sum\limits_{i^{\prime} \in {M{(j)}}}^{\;}\left( {v_{i^{\prime}} - \; {\hat{\mu}}_{j}} \right)^{2}}}},{{\hat{C}}_{j,n} = {\frac{1}{{{M(j)}} - 1}{\sum\limits_{i^{\prime} \in {M{(j)}}}^{\;}{\left( {v_{i^{\prime}} - \; {\hat{\mu}}_{j}} \right)\left( {{\underset{\_}{v}}_{n{(i^{\prime})}} - \; \hat{\mu}} \right)}}}},{{\hat{C}}_{n} = {\frac{1}{{{M(j)}} - 1}{\sum\limits_{i^{\prime} \in {M{(j)}}}^{\;}{\left( {{\underset{\_}{v}}_{n{(i^{\prime})}} - \; \hat{\mu}} \right)^{\prime} \cdot \left( {{\underset{\_}{v}}_{n{(i^{\prime})}} - \; \hat{\mu}} \right)}}}}} & (7) \end{matrix}$

In case cross coupling effects and program disturb effects between neighboring cells are mitigated during programming, the CVD parameters are the same for all cells and estimation is simplified as follows:

{circumflex over (μ)}_(i,j)={circumflex over (μ)}_(j), {circumflex over (σ)}_(i,j)={circumflex over (σ)}_(j)  (8)

Note that other estimation algorithms can be applied in order to estimate the CVD parameters. For example, a more optimal MAP estimation can be used instead of the LMMSE estimation. In this case, the state estimates (derived from L _(e)) are used in order to divide the cells into subsets of cells characterized by having the same state and the same neighboring cell states. Then the CVD parameters of each such cell population can be estimated very simply, for example by computing an empirical expectation value and variance of each population.

In the examples above, the extrinsic estimates were used in order to produce “hard” decisions on the states. A more complex and accurate scheme can utilize the soft state estimates. For example, the CVD parameters based on soft values of the L _(ei) may be estimated based on only some of the cells, for example only on the more reliable cells. This results in simpler processing (less information is processed) and more accurate results. We can choose the cells that will be used for the CVD parameters estimation as the cells whose extrinsic state estimation is more reliable (i.e. the cells for which max|L _(ei)| is higher). One optimal scheme uses the soft state estimation as part of the CVD parameters estimation (without performing hard decisions) based on Bayesian estimation techniques (S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory, Prentice-Hall Inc., 1993—chapters 10-12). Bayesian estimation techniques allow utilization of a-priori statistics of the estimated parameters (in the present case, a-priori probabilities for the cell to be programmed to each state).

Additional details on how to compute CVD parameters, given an estimate of the read cell voltages and the programmed cell states, can be found in U.S. Ser. No. 11/941,945 and in U.S. Ser. No. 11/860,553.

2) Soft States Estimation Block

This block computes a-priori soft estimates of the programmed cells' states based on the read cell voltages and on the estimated cells' CVD parameters. For example in the GMM model described in (2), we can compute the soft state estimate for each cell as follows:

$\begin{matrix} {{{\Pr \left( {{{v_{i}s_{i}} = S_{j}},{\overset{\bigwedge}{\underset{\_}{\theta}}}_{i}} \right)} = {\int_{{LTH}{(v_{i})}}^{{UTH}{(v_{i})}}{\frac{1}{\sqrt{2\pi {\hat{\sigma}}_{i,j}^{2}}}^{- \frac{{({v^{\prime} - {\hat{\mu}}_{i,j}})}^{2}}{2{\hat{\sigma}}_{i,j}^{2}}}\ {v^{\prime}}}}},{{\Pr \left( {{v_{i}{s_{i} \neq S_{j}}},{\overset{\bigwedge}{\underset{\_}{\theta}}}_{i}} \right)} = {1 - {\Pr \left( {{{v_{i}s_{i}} = S_{j}},\overset{\bigwedge}{{\underset{\_}{\theta}}_{i}}} \right)}}}} & (9) \end{matrix}$

The terms in (9) can then be substituted in (3) in order to compute the a-priori soft estimates L _(ai).

3) ECC Decoding Block

This block computes the a-posteriori soft estimates L _(di) based on the a-priori state estimates L _(ai) and based on the assumption that the stored bits constitute valid codewords. In practice iterative ECC schemes can be used for this. In such a scheme an iterative decoder can approximately compute L _(d) based on L _(a). Such a code can operate directly on the cell states. However, due to complexity considerations it is more common to use a suboptimal decoder that operates on soft bit estimates (as opposed to soft state estimates). Let b_(i,j) denote the j'th bit stored in the i'th cell. Then such a decoder can operate on a-priori soft bit LLR estimates defined as

$L_{a_{i,j}} = {\log \frac{\Pr \left( {{{v_{i}b_{i,j}} = 0},{\overset{\bigwedge}{\underset{\_}{\theta}}}_{i}} \right)}{\Pr \left( {v_{i}{b_{i,j} \neq {1_{,}{\overset{\bigwedge}{\underset{\_}{\theta}}}_{i}}}} \right)}}$

to produce a-posteriori soft bit LLR estimates defined as

$L_{d_{i,j}} = {\log {\frac{\Pr \left( {{{v_{i}b_{i,j}} = 0},{\overset{\bigwedge}{\underset{\_}{\theta}}}_{i},{\underset{\_}{c} \in C}} \right)}{\Pr \left( {{{v_{i}b_{i,j}} = {1_{,}{\overset{\bigwedge}{\underset{\_}{\theta}}}_{i}}},{\underset{\_}{c} \in C}} \right)}.}}$

The a-priori soft bit estimates can be computed as follows:

$L_{a_{i,j}} = {{\log \frac{\Pr \left( {{{v_{i}b_{i,j}} = 0},{\underset{\_}{\hat{\theta}}}_{i}} \right)}{\Pr \left( {{v_{i}{b_{i,j} \neq 1}},{\underset{\_}{\hat{\theta}}}_{i}} \right)}} = {\log \frac{\sum\limits_{S_{j} = 0}^{\;}\; {\Pr \left( {{{v_{i}s_{i}} = S},{\underset{\_}{\hat{\theta}}}_{i}} \right)}}{\sum\limits_{S_{j} = 1}^{\;}\; {\Pr \left( {{{v_{i}s_{i}} = S},{\underset{\_}{\hat{\theta}}}_{i}} \right)}}}}$

The a-posteriori soft bit estimates can be translated into approximate a-posteriori state estimates by ignoring the statistical dependencies between these bit estimates (originating from the fact that the bits belong to the same cell and were subjected to the same noises). This can be done simply by estimating the state ŝ_(i) of cell ‘i’ by taking the hard decisions of the extrinsic bit estimates, for the bits stored in the i'th cell, and mapping the hard decisions to a state based on the mapping used during programming. Alternatively, approximate soft state estimates can be computed. For example, in the four-bits-per-cell case, the a-posteriori soft state estimate of the i'th cell can be approximated as follows:

${{\Pr \left( {{s_{i} = {{b_{0}b_{1}b_{2}b_{3}}\underset{\_}{v}}},\underset{\_}{\hat{\theta}},{\underset{\_}{c} \in C}} \right)} \cong {\prod\limits_{j = 0}^{3}\; {\Pr \left( {{b_{i,j} = {b_{j}\underset{\_}{v}}},\underset{\_}{\hat{\theta}},{\underset{\_}{c} \in C}} \right)}}},{{{where}\mspace{14mu} b_{{j = 0},1,2,3}} \in \left\{ {0,1} \right\}}$

Note that using an ECC decoder that operates on the bits stored in the cells instead of the states programmed to the cells is sub-optimal, because information regarding the statistical dependencies between bits stored in the same cell is lost. An optimal scheme would use a decoder that operates directly on the programmed states. Such a decoder is described below in connection with FIG. 8.

An alternative exemplary scheme is shown in FIG. 2. According to this scheme, we first generate corrected estimates of the cells read voltages {circumflex over (v)} by canceling the cross coupling effects and the PD effects of neighboring cells and then estimate each cell's state based on CVD parameters which are fixed for all cells. The scheme shown in FIG. 2, includes the following three blocks that replace the CVD parameters estimation block and the soft states estimation block shown in FIG. 1:

1) CVD Parameters Estimation Block

This block estimates fixed CVD parameters for all cells (instead of different parameters for each cell as in FIG. 1). Hence, this block has lower complexity compared to the equivalent block in FIG. 1. For example, under the GMM CVD model described by (2) and assuming an LMMSE cross coupling and program disturb canceller, the estimated parameters are:

{circumflex over (θ)}=[{circumflex over (θ)} ₁ . . . {circumflex over (θ)} _(L)], where {circumflex over (θ)} _(j)=[{circumflex over (μ)}_(j) {tilde over (σ)}_(j) α _(j)] and {tilde over (σ)}_(j)={circumflex over (σ)}_(j)−α _(j)·Ĉ*_(j,n), α _(j)=Ĉ_(j,n)·Ĉ_(n) ⁻¹ and {circumflex over (μ)}_(j), {circumflex over (σ)}_(j), Ĉ_(j,n), Ĉ_(n) are defined in (7) Hence, the number of estimated parameters in this example is proportional to the number of states L instead of the number of cells M.

2) Cross Coupling Canceller Block

This block computes a corrected value of the i'th cell's voltage by cancelling the cross coupling effects and the PD effects of its neighboring cells. Under the GMM CVD model described by (2) and assuming an LMMSE cross coupling and program disturb canceller, this is performed as follows:

Based on the estimated state of the i'th cell ŝ_(i)=S_(j) the cross coupling and program disturb canceller block chooses the correct coefficients α _(j) and performs the following computation:

{circumflex over (v)} _(i) =v _(i)−α _(j)·( v _(n(i))−{circumflex over (μ)})  (10)

Note that various variants of the cross coupling and program disturb canceller block can be implemented. In some cases cancelling the effect of neighboring cells on the target cell can be improved by knowing the programmed state of the neighboring cells and not only the read voltages of the neighboring cells. Two examples of this are:

A. Mitigation of PD noises by identifying cells that are more prone to PD and adapting the computation of their corrected voltage {circumflex over (v)} accordingly (for example applying stronger correction to their read voltage). PD noise of a cell is usually a function of the programmed states of its neighboring cells, where certain patterns result in higher probability for strong PD. Hence, identifying cells which are more prone to PD requires knowing the programmed state of their neighboring cells. Thus, by utilizing the extrinsic estimates of the cells' states we can identify cells that are more prone to PD and improve the estimation of {circumflex over (v)}.

B. Cancellation of cross coupling effects in all-bit-line (ABL)-type Flash devices. In this type of device all bit lines in a word line are programmed simultaneously (as opposed to conventional Flash devices in which odd and even bit lines are programmed separately). As a result the cross coupling effect of a cell on its neighboring cell in the same word line is less predictable based on its read voltage. The cross coupling effect is a function of the amount of change in the charge of the “disturbing” cell that occurred after the target cell was inhibited (finished its programming). Hence in an ABL device in which all the cells in a word line are programmed simultaneously we need to predict the amount of charge change of a neighboring cell after the target cell was inhibited in order to provide better cross coupling cancellation. Such prediction can be improved if we know the programmed state of the neighbor and target cells. For example if we know that the neighbor cell was programmed to a lower state and the target cell was programmed to a higher state then the probability that the neighbor cell affected the target cell is low because most likely the neighbor cell was inhibited before the target cell. On the other hand, if we know that the neighbor cell was programmed to a higher state and the target cell was programmed to a lower state then the probability that the neighbor cell affected the target cell is high since most likely the neighbor cell was inhibited after the target cell. This knowledge can be employed in order to improve the cross coupling cancellation (i.e. the estimation of {circumflex over (v)}), by taking into account also the relation between the programmed states of a target cell and its neighbors. In this case (10) looks like:

$\begin{matrix} {{{\hat{v}}_{i} = {v_{i} - {{\underset{\_}{\alpha}}_{j} \cdot \left\lbrack {\left( {{\underset{\_}{v}}_{n{(i)}} - v_{i}} \right) - {\hat{\mu}}_{\Delta \; {n{(i)}}}^{j}} \right\rbrack}}},{{\hat{\mu}}_{\Delta \; {n{(i)}}}^{j} = {\sum\limits_{\;_{{\underset{\_}{v}}_{n{(i)}} \geq {\hat{\mu}}_{j}}}^{\;}\; \left\{ \left( {{\underset{\_}{v}}_{n{(i)}} - {\hat{\mu}}_{j}} \right) \right\}}}} & (11) \end{matrix}$

Note that in (11) the term {circumflex over (μ)}_(Δn(i)) ^(j) is a function of the state s_(j) that cell i was programmed to, meaning that {circumflex over (μ)}_(Δn(i)) ^(j) is the average charge (voltage) that neighboring cells, in the same word-line, accumulate after the target cell i (for which voltage v_(i) was read from) was inhibited. As j increases so the cross coupling effect decreases. When j=L, i.e. the highest state, is considered as the target cell, no other states are likely to be programmed after it, and hence cells in S_(L) suffer the least from the cross coupling effect from neighboring cells in the same word line. The target cells can still suffer from neighboring cells in adjacent word-lines that are entirely programmed after the word line which cell i belongs to has finalized its programming sequence. More details on digital cross coupling cancellation can be found in U.S. Ser. No. 11/860,553.

3) Soft States Estimation Block

This block is similar to the corresponding block in FIG. 1, except that CVD parameters are fixed for all cells while the corrected cells' voltages {circumflex over (v)} are employed for the computation of the a-priori soft states estimation. Hence, in the GMM model described in (2), we can compute the a-priori soft state estimate for each cell as follows:

$\begin{matrix} {{{\Pr \left( {{{{\hat{v}}_{i}s_{i}} = S_{j}},\underset{\_}{\hat{\theta}}} \right)} = {\int_{{LTH}{({\hat{v}}_{i})}}^{{UTH}{({\hat{v}}_{i})}}{\frac{1}{\sqrt{2\pi {\overset{\sim}{\sigma}}_{j}^{2}}}^{- \frac{{({v^{\prime} - {\hat{\mu}}_{j}})}^{2}}{2{\overset{\sim}{\sigma}}_{j}^{2}}}\ {v^{\prime}}}}},{{\Pr \left( {{{\hat{v}}_{i}{s_{i} \neq S_{j}}},\underset{\_}{\hat{\theta}}} \right)} = {1 - {\Pr \left( {{{{\hat{v}}_{i}s_{i}} = S_{j}},\underset{\_}{\hat{\theta}}} \right)}}}} & (12) \end{matrix}$

The terms in (12) can then be substituted in (3) in order to compute the a-priori soft state estimates L _(ai).

The iterative schemes described above can also be described in the context of factor graphs and message passing decoding (Kschischang, F. R.; Frey, B. J.; Loeliger, H. A., Factor graphs and the sum-product algorithm, IEEE Transactions on Information Theory, vol. 47, pp. 498-519, February 2001). This is an equivalent description that is commonly used for iterative schemes. In this setting, the various unknown parameters which require estimation (such as CVD parameters, programmed cell states and stored bits) and the various constraints on the parameters (such as the constraints posed by the physics of the cell and the constraints posed by the ECC code) appear as nodes in a factor graph while edges are connected between parameters and their constraints. An iterative message passing algorithm is used in order to find the unknown parameters by exchanging information between the parameters and their constraints along the graph edges. These messages carry estimates of the parameters that are updated iteratively. The algorithm is iterated until convergence of the parameters to values that satisfy all constraints, or until some maximal number of iterations is reached. FIG. 3 shows a factor graph that is equivalent to the scheme illustrated in FIG. 1.

FIG. 4 is a high-level schematic block diagram of a flash memory device. A large number of individually addressable memory cells are arranged in a regular array 11 of rows and columns. Individual memory cells can be controlled by bit lines, select gates arranged in word lines, and steering gates. Bit lines are designated herein to extend along columns of array 11, and word lines are designated to extend along the rows of array 11. Bit line unit 13 may include a bit line decoder, storage elements, driver circuits and sense amplifiers. Bit line unit 13 can be coupled to cell array 11 by line 15, and to controller 27 by bit-control line 29 and by read line 41. Word line unit 19 may include a select gate decoder and driver circuits. Word line unit 19 can be coupled to cell array 11 by line 17, and to controller 27 by word-control line 31. Steering line unit 43 may include a steering gate decoder and driver circuits. Steering unit 43 can be coupled to cell array 11 by line 23, to controller 27 by steering-control line 33, and to bit line unit 13 by line 44. Bit line unit 13, word line unit 19 and steering unit 43 can be coupled to bus 25, which in turn is coupled to controller 27. Controller 27 can be coupled to the host by line 35.

When a preselected memory cell is to be programmed, voltages can be applied to the bit lines, word line and steering gates, corresponding to the preselected memory cell, at predetermined levels sufficient for the programming of the preselected cell. Controller 27 sends the address of the preselected memory cell through bus 25 to the respective decoders in bit line unit 13, word line unit 19, and steering gate unit 43 through lines 26 a, 26 b, and 26 c, respectively. Status and control commands between bit line unit 13, word line unit 19, steering gate unit 43 and controller 27 are communicated through bit-control line 29, word-control line 31 and steering control line 33.

When a preselected memory cell is to be read, voltages can be applied to the corresponding bit lines, word line and steering gates, corresponding to the preselected memory cell, at predetermined levels, sufficient to enable the reading of the preselected memory cell. Controller 27 is capable of applying the voltages of the bit lines through bit-control line 29, applying the voltages of the word lines through word-control line 31 and applying the voltages of steering gates through steering control line 33. A current can be generated through the preselected memory cell by these voltages. The current is indicative of whether the preselected memory cell was programmed or not (in the case of the cells of array 11 having been programmed one bit per cell) or of the bit pattern that has been stored in the preselected memory cell (in the case of the cells of array 11 having been programmed with more than one bit per cell). The value of the current can be amplified and compared against references by sense amplifiers in bit line unit 13, the result of which can be temporarily stored in latches or registers. The resultant data, read out from the preselected memory cell, can be sent to controller 27 through read line 41.

In reading the cells of array 11, controller 27 performs joint CVD estimation and error correction as described above. The functional blocks of controller 27 that perform the joint CVD estimation and error correction, as illustrated in FIG. 1 or alternatively as illustrated in FIG. 2, may be implemented in hardware, in firmware, in software, or as a combination of hardware and/or firmware and/or software.

FIG. 5 shows one embodiment of controller 27. This embodiment of controller 27 includes five functional blocks: a measurement functional block 1, an assignment functional block 2, an a-priori metric functional block 3, a decoder 4 and a CVD model estimation block 5. Measurement functional block 1 applies the relevant voltages through bit-control line 29, word-control line 31 and steering control line 33 to obtain, via read line 41, threshold voltage values of the cells of array 11. Assignment functional block 2 assigns each cell to its CVD model population. A-priori metric functional block 3 corresponds to the soft states estimation block of FIG. 1. Decoder 4 corresponds to the ECC decoding block of FIG. 1. CVD model estimation block 5 corresponds to the CVD parameters estimation block of FIG. 1. In an alternative embodiment, all the cells are deemed to belong to the same CVD model population, and assignment functional block 2 either is inactivated or is absent.

FIG. 6 shows another embodiment of controller 27. This embodiment of controller 27 includes three functional blocks: a measurement functional block 6, an assignment functional block 7, and a constrained CVD model estimation block 8. Measurement functional block 6 applies the relevant voltages through bit-control line 29, word-control line 31 and steering control line 33 to obtain, via read line 41, threshold voltage values of the cells of array 11. These threshold voltages are indicative of the bit patterns stored in the cells. Assignment functional block 7 assigns each cell to its CVD model population. Constrained CVD model estimation block 8, that corresponds to the functional blocks illustrated in FIG. 1, estimates the CVD models under the constraint that the bit patterns collectively must be a valid error correction codeword. In an alternative embodiment, all the cells are deemed to belong to the same CVD model population, and assignment functional block 7 either is inactivated or is absent.

FIG. 7 is a high-level block diagram of a system 50 of the present invention. System 50 includes a processor 52 and four memory devices: a RAM 54, a boot ROM 56, a mass storage device (hard disk) 58 and a flash memory device of FIG. 4 as a flash memory device 62, all communicating via a common bus 64. In system 50, controller 27 of flash memory device 62 functions only as an interface to bus 64; the rest of the functionality of flash controller 27 of FIG. 2B as described above is emulated by flash memory driver code 60 that is stored in mass storage device 58 and that is executed by processor 52 to interface between user applications executed by processor 52 and flash memory device 62, and to manage the flash memory of flash memory device 62. In addition to the conventional functionality of such flash management driver code, driver code 60 emulates the functionality of controller 27 of FIG. 4 with respect to joint CVD estimation and error correction as described above. Driver code 60 typically is included in operating system code for system 50 but also could be freestanding code.

The components of system 50 other than flash memory device 62 constitute a host 70 of flash memory device 62. Mass storage device 58 is an example of a computer-readable storage medium bearing computer-readable driver code for joint CVD estimation and error correction. Other examples of such computer-readable storage media include read-only memories such as CDs bearing such code.

The joint CVD estimation and ECC presented above is an example of constrained decoding. Specifically, the CVD estimation and the ECC constrain each other. The CVD estimation is constrained by the condition that the bits stored in the cells are supposed to represent a valid codeword. The ECC is constrained by the a-priori bit estimates being according to a given CVD model.

In an alternative method of reading flash memory cells, the ECC is constrained by the additional knowledge that each bit shares a cell with one or more other bits. Knowing which bits are stored together in the same cell is a-priori knowledge that is in addition to the ECC constraint that all the bits of all the cells taken collectively are supposed to represent a valid codeword. FIG. 8 shows an example of a tripartite graph for exchanging messages between cell nodes (on the left), bit nodes (in the center) and check nodes (on the right) to decode the bits stored in the cells (in this example eight cells) that correspond to the cell nodes.

The input to the decoding is the threshold voltages of the cells, as read, and a CVD model. The message passing rules are as follows:

Cell Node to Bit Node Message A_(c):

$\begin{matrix} {A_{c} = {\log \frac{\begin{matrix} {\sum\limits_{s \in S}\; {{\Pr \left\lbrack {{s_{m} = {{sc} = 0}},v_{m}} \right\rbrack} \cdot}} \\ {\exp \left\{ {\sum\limits_{c^{\prime} \in {{N_{R}{(m)}}\backslash c}}\; {\left( {1 - c^{\prime}} \right) \cdot E_{c^{\prime}}}} \right\}} \end{matrix}}{\begin{matrix} {\sum\limits_{s \in S}\; {{\Pr \left\lbrack {{s_{m} = {{sc} = 0}},v_{m}} \right\rbrack} \cdot}} \\ {\exp \left\{ {\sum\limits_{c^{\prime} \in {{N_{R}{(m)}}\backslash c}}\; {\left( {1 - c^{\prime}} \right) \cdot E_{c^{\prime}}}} \right\}} \end{matrix}}}} & (13) \end{matrix}$

c indexes the codeword bits. m indexes the cells. s_(m), the state stored in the m-th cell, is a function of the sequence of bits c′εN_(R)(m) that are stored in the m-th cell (“N_(R)(m)” means the right-side neighbors (bit nodes) of cell node m in the tripartite graph). In both the numerator and the denominator, the outer sum is over all the possible states of the cell. Pr[s_(m)=s|c=0,v_(m)] is the probability of the cell being in state s, given that the cell's threshold voltage is v_(m) and that the bit c is 0. Pr[s_(m)=s|c=1,v_(m)] is the probability of the cell being in state s, given that the cell's threshold voltage is v_(m) and that the bit c is 1. The sum in the exponential is over the other bit values of state s (that is what the “\c” means). The E_(c′)s are the corresponding bit-node-to-cell-node messages as defined below. So, for example, in the case of a four-state cell that stores two bits, with the bit patterns of the four states being 00, 01, 10 and 11, if c is the most significant bit (the bit on the left), then

$A_{c} = {\log \frac{\begin{matrix} {\sum\limits_{s \in S}\; {\Pr \left\lbrack {{s_{m} = {{00c} = 0}},v_{m}} \right\rbrack}} \\ {{{\cdot \exp}\left\{ E_{c^{\prime}} \right\}} + {\Pr \left\lbrack {{s_{m} = {{01c} = 0}},v_{m}} \right\rbrack}} \end{matrix}}{\begin{matrix} {\sum\limits_{s \in S}\; {{\Pr \left\lbrack {{s_{m} = {{10c} = 1}},v_{m}} \right\rbrack} \cdot}} \\ {{\exp \left\{ E_{c^{\prime}} \right\}} + {\Pr \left\lbrack {{s_{m} = {{11c} = 1}},v_{m}} \right\rbrack}} \end{matrix}}}$

Using the GMM model of (2), with all states s equally probable,

${\Pr \left\lbrack {{s_{m} = {{sc} = {0/1}}},v_{m}} \right\rbrack} = \frac{{\Pr \left\lbrack {{c = {0/1}},{{v_{m}s_{m}} = s}} \right\rbrack} \cdot {\Pr \left\lbrack {s_{m} = s} \right\rbrack}}{\Pr \left\lbrack {{c = {0/1}},v_{m}} \right\rbrack}$

The term

$\frac{\Pr \left\lbrack {s_{m} = s} \right\rbrack}{\Pr \left\lbrack {{c = {0/1}},v_{m}} \right\rbrack}$

cancels between the numerator of A_(c) and the denominator of A_(c), so that

$\begin{matrix} {A_{c} = {\log \frac{\begin{matrix} {\sum\limits_{s \in S}\; {{\Pr \left\lbrack {{c = 0},{{v_{m}s_{m}} = s}} \right\rbrack} \cdot}} \\ {\exp \left\{ {\sum\limits_{c^{\prime} \in {{N_{R}{(m)}}\backslash c}}\; {\left( {1 - c^{\prime}} \right) \cdot E_{c^{\prime}}}} \right\}} \end{matrix}}{\begin{matrix} {\sum\limits_{s \in S}\; {{\Pr \left\lbrack {{c = 1},{{v_{m}s_{m}} = s}} \right\rbrack} \cdot}} \\ {\exp \left\{ {\sum\limits_{c^{\prime} \in {{N_{R}{(m)}}\backslash c}}\; {\left( {1 - c^{\prime}} \right) \cdot E_{c^{\prime}}}} \right\}} \end{matrix}}}} & (14) \end{matrix}$

The term Pr[c=0/1,v_(m)|s_(m)=s] is given by:

${\Pr \left\lbrack {{c = {0/1}},{{v_{m}s_{m}} = s}} \right\rbrack} = \left\{ \begin{matrix} {{\frac{1}{\sqrt{2\pi \; \sigma_{s}^{2}}}{\exp \left( \frac{\left( {v_{m} - \mu_{s}} \right)^{2}}{2\sigma_{s}^{2}} \right)}\mspace{14mu} {if}\mspace{14mu} {the}}\mspace{11mu}} \\ {\; {{bit}\mspace{14mu} {corresponding}\mspace{14mu} {to}\mspace{14mu} c\mspace{14mu} {in}\mspace{14mu} {state}}} \\ {s\mspace{14mu} {is}\mspace{14mu} {0/1}} \\ {0\mspace{14mu} {otherwise}} \end{matrix} \right.$

Bit Node to Check Node Message D_(ci):

$\begin{matrix} {D_{ct} = {A_{c} + {\sum\limits_{t^{\prime} \in {{N_{R}{(c)}}\backslash t}}\; E_{t^{\prime}c}}}} & (15) \end{matrix}$

t indexes the check nodes. The sum is over the check nodes to which bit node c is connected except the check node t to which the bit node is sending the message D_(ct). (“N_(R)(c)” means the right-side neighbors of bit node c.)

Check Node to Bit Node Messages E_(tc):

$\begin{matrix} {E_{tc} = {\phi^{- 1}\left( {\sum\limits_{c^{\prime} \in {{N_{L}{(t)}}\backslash c}}\; {\phi \left( D_{c^{\prime}t} \right)}} \right)}} & (16) \end{matrix}$

The sum is over the bit nodes to which check node t is connected except the bit node c to which the check node is sending the message E_(tc). (“N_(L)(t)” means the left-side neighbors of check node t.) φ is as in conventional low-density parity check (LDPC) decoding:

${\phi (x)} = \left\{ {{{sign}(x)},{- {{\log \tanh}\left( \frac{x}{2} \right)}}} \right\}$

and operations in the φ domain are done over the group {0,1}×R⁺ (this basically means that the summation here is defined as summation over the magnitudes and XOR over the signs).

Bit Node to Cell Node Messages E_(c):

$\begin{matrix} {E_{c} = {\sum\limits_{t \in {N_{R}{(c)}}}\; E_{tc}}} & (17) \end{matrix}$

The sum is over all the check-node-to-bit-node messages that bit node c received in the most recent exchange of messages between bit nodes and check nodes.

The actual output of the decoding (LLR estimates of the decoded bits) is D_(c)=A_(c)+E_(c). The D_(c) are a-posteriori LLR estimates of the decoded bits. The A_(c) are a-priori LLR estimates of the bits that are provided to the ECC decoding side of the tripartite graph of FIG. 8. E_(c)=D_(c)−A_(c) are extrinsic LLR estimates of the bits that are fed back to the cell nodes. FIG. 9 is a schematic diagram of this iteration between LLR estimation from the read cell voltages v_(m) and ECC decoding.

The check-node-to-bit-node messages E_(tc) all are initialized to zero. Hence, the bit node to cell messages E_(c) also initially all are zero, and the initial values of A_(c) are:

$A_{c} = {\log \frac{\sum\limits_{s \in S}\; {\Pr \left\lbrack {{s_{m} = {{sc} = 0}},v_{m}} \right\rbrack}}{\sum\limits_{s \in S}\; {\Pr \left\lbrack {{s_{m} = {{sc} = 1}},v_{m}} \right\rbrack}}}$

That these initial values of A_(c) are a-priori estimates of LLR values of the bits, can be appreciated by considering that when E_(c)=0, D_(c)=A_(c).

One preferred message exchange schedule is as follows:

1. Send all cell-node-to-bit-node messages.

2. Exchange bit-node-to-check-node messages and check-node-to-bit-node messages according to a conventional LDPC schedule, for example a serial LDPC schedule, for a small number of iterations, possibly as few as one iteration.

3. Send all bit-node-to-cell-node messages.

4. Go to step 1.

At the end of step 2, check for convergence to a valid codeword. If the decoder output (the set of D_(c)'s) corresponds to a valid codeword, then stop. Otherwise, proceed to step 3.

The above is only one exemplary decoding schedule. Another option is to interleave the message exchange between bit nodes and check nodes with the message exchange between bit nodes and cell nodes: after all the bit nodes connected to one cell or to a small group of cells have exchanged messages once with the associated check nodes, those bit nodes exchange messages with the associated cell(s).

Finally, all the constraints may be applied together, with the GMM parameters μ_(s) and σ_(s) being updated as described above, via intermediate LLR estimates D_(c) of the bits, after one or several message exchanges between the bit nodes and the check nodes, and after corresponding changes to the estimated states of the cells.

FIG. 10 illustrates an embodiment of controller 27 that implements decoding constrained by knowledge of which bits are stored in which cells. This embodiment of controller 27 includes four functional blocks: a measurement functional block 101, an assignment functional block 102, a decoder 103 and a CVD model estimation block 104. Measurement functional block 101 applies the relevant voltages through bit-control lines 29, word-control lines 31 and steering control lines 33 to obtain, via read line 41, threshold voltage values of the cells of array 11. Assignment functional block 102 assigns a LLR measure to each bit, for example the initial A_(c) values described above. Decoder 103 implements the constrained decoding, for example by exchanging messages among the nodes of the tripartite graph of FIG. 8 as described above. CVD model estimation block 104 estimates the GMM parameters μ_(s) and σ_(s) from the threshold voltage values of the cells and optionally updates these estimates in cooperation with the decoding by decoder 103.

A limited number of embodiments of methods for joint CVD estimation and error correction, and of a device and system that use the methods, have been described. It will be appreciated that many variations, modifications and other applications of the methods, device and system may be made. 

1. A method of reading a plurality of memory cells that have been programmed to store a codeword of an error correction code, with each cell storing a respective plurality of bits of the codeword, comprising: (a) measuring a respective value of an operational parameter of each cell; (b) assigning each bit of each cell a respective metric, based at least in part on the respective value of the operational parameter of the each cell; and (c) decoding the metrics with reference both to the error correction code and to mutual constraints of the metrics within each cell that are independent of the error correction code.
 2. The method of claim 1, wherein the respective metrics are soft estimates of values of the bits.
 3. The method of claim 2, wherein the respective metrics are log likelihood ratio estimates of the values of the bits.
 4. The method of claim 1, wherein the operational parameters are threshold voltages.
 5. The method of claim 1, wherein the assigning of the respective metrics is in accordance with a cell distribution model of the operational parameter.
 6. The method of claim 5, wherein the operational parameter is a threshold voltage.
 7. The method of claim 5, further comprising: (d) updating the cell distribution model in accordance with the decoding.
 8. The method of claim 7, wherein the decoding and the updating are effected without repeating the measuring of the respective values of the operational parameter.
 9. The method of claim 1, wherein the decoding produces extrinsic estimates of the metrics.
 10. A memory device comprising: (a) a plurality of cells for storing a codeword of an error correction code, with each cell storing a respective plurality of bits of the codeword; (b) circuitry for measuring a respective value of an operational parameter of each cell; and (c) a controller operative: (i) to instruct the circuitry to measure the values of the operational parameters, (ii) to assign each bit of each cell a respective metric, based at least in part on the respective value of the operational parameter of the each cell, and (iii) to decode the metrics with reference both to the error correction code and to mutual constraints of the metrics within each cell that are independent of the error correction code.
 11. A memory controller, for a memory that includes a plurality of cells for storing a codeword of an error correction code, with each cell storing a respective plurality of bits of the codeword, the memory controller comprising: (a) a measurement functional block for obtaining, from the memory, for each cell, a measurement of a respective value of an operational parameter of the cell; (b) an assignment functional block for assigning each bit of each cell a respective metric, based at least in part on the respective value of the operational parameter of the each cell; and (c) a decoder for decoding the metrics with reference both to the error correction code and to mutual constraints of the metrics within each cell that are independent of the error correction code.
 12. A system for managing a first memory that includes a plurality of cells for storing a codeword of an error correction code, with each cell storing a respective plurality of bits of the codeword, the system comprising: (a) a second memory for storing program code for: (i) obtaining, from the first memory, for each cell, a measurement of a respective value of an operational parameter of the cell, (ii) assigning each bit of each cell a respective metric, based at least in part on the respective value of the operational parameter of the each cell, and (iii) decoding the metrics with reference both to the error correction code and to mutual constraints of the metrics within each cell that are independent of the error correction code; and (b) a processor for executing the code.
 13. A computer-readable storage medium having computer-readable code embodied on the computer-readable storage medium, the computer-readable code for managing a memory that includes a plurality of cells for storing a codeword of an error correction code, with each cell storing a respective plurality of bits of the codeword, the computer-readable code comprising: (a) program code for obtaining from the memory, for each cell, a measurement of a respective value of an operational parameter of the cell; (b) program code for assigning each bit of each cell a respective metric, based at least in part on the respective value of the operational parameter of the each cell; and (c) program code for decoding the metrics with reference both to the error correction code and to mutual constraints of the metrics within each cell that are independent of the error correction code. 